Quantum Mechanical effect of transitioning through a classically forbidden energy state.
One of the most popular applications is in electron-tunneling microscopes (see
scanning tunneling microscope) that are used to see objects that are too small to see using conventional microscopes. Electron tunneling microscopes overcome the limiting effects conventional microscopes (optical aberrations, wavelength limitations) by scanning the surface of an object with tunneling
electrons.
See also Quantum Mechanics.
~cmjr - just to get started